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$\begingroup$What is your ultimate objective with "characterizing" the data? Definitely read Spikes when you have a chance. The short answer from there is that it depends on what you are looking to get out of the signal. If you're looking to drive a device or something of that nature, the FFT is going to be computationally burdensome, and may not give you sufficient information.$\endgroup$
– Chuck SherringtonMay 28 '14 at 21:43

$\begingroup$I'm using "information" as a loaded term. I was referring to both measures that you are talking about, sorry if that wasn't clear. Neither is going to tell you anything meaningful. If you're locking to a specific event (sensory input or specific motor output - e.g., an EMG of a muscle) the frequency variation will tell you something, but a "free form" recording really isn't. You'd be better off examining local field potentials (most extracellular recording systems can separate these out in the spike sorting processing) if you are trying to tease out frequency changes.$\endgroup$
– Chuck SherringtonMay 29 '14 at 20:02

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$\begingroup$Otherwise, this is really just an exercise in signal processing, to be frank.$\endgroup$
– Chuck SherringtonMay 29 '14 at 20:03

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$\begingroup$(not trying to be an overbearing curmudgeon here, just offering some constructive criticism. I'm happy to see a methods question on here!)$\endgroup$
– Chuck SherringtonMay 29 '14 at 21:00

2 Answers
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For binary data (spike-trains), people use a spike-train autocovariance function (same as autocorrelation but subtracting the mean firing rate). It's commonly used to study brain oscillations (e.g. Engel & Konig, 1991). There is a good description of the math in the Dayan & Abbott (page 27).

As this answer explains, the Fourier transform of the autocorrelation of $x$ is the same as the magnitude squared of the Fourier transform of $x$. The autocorrelation of x can be expressed as $x(t)*x(-t)$, where * means convolution and the Fourier transform of the autocorrelation is then $X(w)X^*(w)=|X(w)^2|$, which of course is the Fourier transform of the original signal $x(t)$.